Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an1p)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.an1p.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(9/2), -(5/2)}, -z] == (1/22325625) (22325625 - 53581500 z + 196465500 z^2 - 2724321600 z^3 - 61297236000 z^4 - 1389404016000 z^5 + 11679414364800 z^6 - 23643649612800 z^7 + 20793330996480 z^8 - 9744430348800 z^9 + 2695335955200 z^10 - 465611408640 z^11 + 51727660320 z^12 - 3727509408 z^13 + 172037760 z^14 - 4875520 z^15 + 76800 z^16 - 512 z^17) + (1/22325625) ((16 Sqrt[Pi] (239987966400 z^(11/2) - 1175325681600 z^(13/2) + 1948107445200 z^(15/2) - 1545292047600 z^(17/2) + 681871818600 z^(19/2) - 181639984680 z^(21/2) + 30612850695 z^(23/2) - 3344446665 z^(25/2) + 238199010 z^(27/2) - 10902360 z^(29/2) + 307104 z^(31/2) - 4816 z^(33/2) + 32 z^(35/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]